How Does Cloth Friction Work?
Here's a simulation of the situation (Blender 2.75).



The parameters that I cosidered in this "catalogue" are:


Resolution of surfaces (unsubdivided-> first row; Collision object subdivided-> second Row; Cloth object subdivided-> third row; Both subdivided-> fourth row)
Friction (0.1 or 80)
Repel Distance (0.001 or 1)




By comparing the elements of the first row, I can say that it seems to be at least a little difference of the behavior when friction jumps from 0.1 to 80 (but is not that strong as one expect)

Look at the last element of the matrix (4-4): it is the one where friction reveal itself in a more convincing way..but there's another, which has the same behavior: 2-4. This led me to think that is also important to consider how many faces your collision object has.

Now compare 2-4 with 2-2... also the max Repel distance influence the behavior.

Conclusion

It seems that changing only the Friction factor is not enough to run the sim as expected, but you have to deal at least with other two parameters:


resolution of collision object (should be enough detailed, but more subd won't give more frictional effect apart from the contribute given by the fact that the faces are in range for a longer period)
repulsion distance (act as a sort of detecting thershold, but more rep dist won't give more frictional effect)


Friction is the value that drives the pover of frictional effect, but it must be supported by other variables in order to affect the sim.

Here's the blend of where the gif comes from: